I have published data on the rates of children looked after (by a local authority) per 10,000 by local authority and over time.
I know that in Lancashire an intervention was conducted in 2021. I can see that the rate is lower after this time.
I want to know whether the rate of children looked after in Lancashire is significantly lower after the intervention. What statistical test can I use to test whether the rate of children looked after is significantly lower post-intervention.
The data I have are:
Year Children Looked After per 10,000 (rate)
2019 85
2020 84
2021 80 (Intervention started this year)
2022 77
2023 74
I have no further information beyond the table above, it would also be possible to compare between local authorities, so to compare Lancashire to an area that did not have the intervention in 2021.
Can you suggest if significance testing is possible here, and what method would you use?
Thank you very much.
I have considered a repeated t-test but felt I didn't know if this would work for a rate as I don't have information on the variance.
I considered regression but was concerned there were not enough time points pre/post intervention.